462 Mr DE morgan, ON THE SYLLOGISM, No. V. AND 



ceptor ; and I think I do nearly as well for him as he could do for himself, if I suppose him 

 to select from the universe ' material object, past or present', as a lot which he defies me 

 to difference from all other things, the following miscellany ; — all men who have killed their 

 brothers, the hundred largest ink-stands that ever were made, and Aristotle's dinner on 

 his twenty-first birthday. What is the class-mark of these objects ? I answer that to 

 them alone belongs the epithet — ' Selected by the fancy of {here insert name and date) 

 in unsuccessful impeachment of the unlimited right of logical division'. I am willing to go 

 further than Nizolius, and to divide species into essential, accidental, and perverse; affirming 

 that the difference is extralogical. The more absurd such an instance as mine, the better 

 does it make the claim asserted ; Hamilton implied the like when he presented Newton and 

 Leibnitz with their wigs awry. 



If the number of objects in the universe be w, the number of possible collections which 

 can be the selections denoted by terms is S'-S, the number of pairs of collections is 

 (2''~'-l)(2"-S) and the whole universe of relations, true and false, has 8(2''~'-l)(2"-3) 

 instances, equally divided between true and false. Let the relations species, e.vient, &c. 

 be denoted by the symbols )), (•( &c : thus X)) and ((X both denote ' species of X'. When 

 a symbol of relation is placed between two others, let it be read in the singular exemplar 

 method; and let the two extremes be read /rom the middle term. Thus (( (•) )-^ or 

 X(( (•) )'(Y means to assert that ' Any one class is either species of X or external of Y': and 

 X)) )) ))Y means 'Any one genus of X is some one species of Y '. Of such possible readings 

 there are 8.8.8, or 512, of which half are restrictives, and half are not. 



I may be asked whether such methods of stating propositions are actually in use.'' 

 I answer yes, sometimes in grave writing, and more often in rhetorical flourish, a kind 

 of appeal to assent in which a little study of the characters of fallacy is not obviously needless. 

 A certain sort of speaker wants to say that all Englishmen are lovers of liberty : for your 

 stump-orator deals in nothing but universals, be the name of his stump what it may ; a 

 proceeding forced upon him by the lovers of his style, who consider a man of rules with 

 exceptions as an equivocator and a loophole- monger. He declaims as follows: — 'Show me any 

 number of men, and I will say with confidence either that they will with one accord raise 

 their voices for liberty, or that there are aliens among them.' This figure of speech is 

 X((Z expressed as X(( (•) ("(Z, where X is ' lover of liberty ' and Z is ' Englishman'. 



Every proposition is a blank syllogism : that is, every true proposition is a conclusion 

 which has middle extents, whether the terms exist for them or not. Thus X))Y is X)) ))Y, 

 where for may be written any genus of X which is also species of Y. It is also X) • (0(*)Y, 

 where for may be written the contrary of any such intermediate class. Even the useless ex- 

 treme X))X may be written X))X))X. And the blank syllogism and the conclusion are con- 

 vertible : thus X))Y is X))0))Y, and X))0))Y is X))Y. When the concrete middle term is 

 inserted, this convertibility ceases: thus X))Y is deducible from X))A))Y, but not X))A))Y 

 from X))Y. The essential of syllogism is the existence of the middle term, not its being this 

 or that. The conclusion, as I have observed in a former paper, renounces all knowledge 

 of the middle except its existence. That ' all man is mortal ' is established by every one 

 who shall prove that a genus of man is a species of mortal : the physiologist may have 



